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                    线性模型
            
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                                <h1 id="&#x897F;&#x74DC;&#x4E66;&#x6982;&#x5FF5;">&#x897F;&#x74DC;&#x4E66;&#x6982;&#x5FF5;</h1>
<h2 id="&#x9644;&#x5F55;">&#x9644;&#x5F55;</h2>
<ul>
<li><p>Page399: &#x884C;&#x5217;&#x5F0F;&#xFF08;determinant&#xFF09;</p>
<p>n &#x9636;&#x65B9;&#x9635; A &#x7684;&#x884C;&#x5217;&#x5F0F;&#xFF08;determinant&#xFF09;&#x5B9A;&#x4E49;&#x4E3A;&#xFF1A;<br><script type="math/tex; ">det(A) = \sum_{\sigma \in S_n} par(\sigma) A_{1\sigma_1}A_{2\sigma_2}...A_{n\sigma_n}</script><br>&#x5176;&#x4E2D;&#xFF0C;Sn &#x4E3A;&#x6240;&#x6709; n &#x9636;&#x6392;&#x5217;&#xFF08;permutation&#xFF09;&#x7684;&#x96C6;&#x5408;&#xFF0C;par(&#x3C3;) &#x7684;&#x503C;&#x4E3A; -1 &#x6216; +1 &#x53D6;&#x51B3;&#x4E8E; &#x3C3; = (&#x3C3;1,&#x3C3;2,...&#x3C3;n) &#x4E3A;&#x5947;&#x6392;&#x5217;&#x6216;&#x5076;&#x6392;&#x5217;&#xFF0C;&#x5373;&#x5176;&#x4E2D;&#x51FA;&#x73B0;&#x964D;&#x5E8F;&#x7684;&#x6B21;&#x6570;&#x4E3A;&#x5947;&#x6570;&#x6216;&#x5076;&#x6570;&#xFF0C;&#x4F8B;&#x5982; (1,3,2) &#x4E2D;&#x964D;&#x5E8F;&#x6B21;&#x6570;&#x4E3A; 1&#xFF0C;(3,1,2) &#x4E2D;&#x964D;&#x5E8F;&#x6B21;&#x6570;&#x4E3A; 2&#x3002;&#x5BF9;&#x4E8E;&#x5355;&#x4F4D;&#x9635;&#xFF0C;&#x6709; det(I) = 1&#x3002;</p>
<p>&#x76F4;&#x89C2;&#x7406;&#x89E3;&#xFF1A;</p>
<ul>
<li>&#x662F;&#x4EC0;&#x4E48;&#xFF1A;&#x4EE5;&#x4E8C;&#x7EF4;&#x4E3A;&#x4F8B;&#xFF0C;&#x8868;&#x793A;&#x4E00;&#x4E2A;&#x533A;&#x57DF;&#x7684;&#x9762;&#x79EF;&#xFF0C;&#x8D1F;&#x6570;&#x5219;&#x662F;&#x5C06;&#x533A;&#x57DF;&#x7FFB;&#x8F6C;&#xFF0C;&#x6216;&#x8005;&#x8BF4;&#x5B9A;&#x5411;&#x6539;&#x53D8;&#x3002;&#x5982;&#x679C;&#x77E9;&#x9635;&#x6240;&#x4EE3;&#x8868;&#x7684;&#x53D8;&#x6362;&#x5C06;&#x7A7A;&#x95F4;&#x538B;&#x7F29;&#x5230;&#x66F4;&#x5C0F;&#x7684;&#x7EF4;&#x5EA6;&#xFF08;&#x4E0D;&#x6EE1;&#x79E9;&#xFF09;&#xFF0C;&#x5219;&#x884C;&#x5217;&#x5F0F;&#x4E3A; 0&#xFF08;&#x6BD4;&#x5982;&#x4E8C;&#x7EF4;&#x5230;&#x4E00;&#x7EF4;&#xFF0C;&#x9762;&#x79EF;&#x5C31;&#x53D8;&#x6210;&#x4E86;&#x96F6;&#xFF09;&#x3002;&#x5217;&#x4EE3;&#x8868;&#x57FA;&#x5411;&#x91CF;&#xFF0C;&#x884C;&#x4EE3;&#x8868;&#x5750;&#x6807;&#xFF0C;&#x4E00;&#x4E2A; m&#xD7;n &#x7684;&#x77E9;&#x9635;&#x8868;&#x793A; n &#x4E2A;&#x57FA;&#x5411;&#x91CF;&#x8868;&#x793A;&#x7684;&#x7A7A;&#x95F4;&#x6620;&#x5C04;&#x5728; m &#x7EF4;&#x7684;&#x5750;&#x6807;&#x4E0A;&#x3002;&#x884C;&#x5217;&#x5F0F;&#x662F;&#x9762;&#x79EF;&#xFF08;&#x4E8C;&#x7EF4;&#xFF09;&#x6216;&#x4F53;&#x79EF;&#xFF08;&#x4E09;&#x7EF4;&#xFF09;&#x7F29;&#x653E;&#x7684;&#x6BD4;&#x4F8B;&#x3002; </li>
<li>&#x600E;&#x4E48;&#x7B97;&#xFF1A;&#x4EE5;&#x4E8C;&#x7EF4;&#x4E3A;&#x4F8B;&#xFF0C;&#x4E3B;&#x5BF9;&#x89D2;&#x7EBF;&#x5143;&#x7D20;&#x4EE3;&#x8868;&#x4E24;&#x4E2A;&#x7EF4;&#x5EA6;&#x7F29;&#x653E;&#x7684;&#x6BD4;&#x4F8B;&#xFF0C;&#x5176;&#x4F59;&#x4E24;&#x4E2A;&#x5143;&#x7D20;&#x4EE3;&#x8868;&#x4E24;&#x4E2A;&#x7EF4;&#x5EA6;&#x7684;&#x5750;&#x6807;&#x533A;&#x57DF;&#x5BF9;&#x89D2;&#x7EBF;&#x7684;&#x7F29;&#x653E;&#x3002;  </li>
</ul>
</li>
<li><p>Page399: &#x8FF9;&#xFF08;trace&#xFF09;</p>
<p>&#x5BF9;&#x4E8E; n &#x9636;&#x65B9;&#x9635; A&#xFF0C;&#x5B83;&#x7684;&#x8FF9;&#xFF08;trace&#xFF09;&#x662F;&#x4E3B;&#x5BF9;&#x89D2;&#x7EBF;&#x4E0A;&#x7684;&#x5143;&#x7D20;&#x4E4B;&#x548C;&#xFF0C;&#x5373;&#xFF1A;<br><script type="math/tex; ">tr(A) = \sum_{i=1}^n A_ii</script></p>
</li>
<li><p>Page400: Frobenius &#x8303;&#x6570;</p>
<p>&#x77E9;&#x9635; A(m&#xD7;n) &#x7684; Frobenius &#x8303;&#x6570;&#x5B9A;&#x4E49;&#x4E3A;&#xFF1A;<br><script type="math/tex; ">\Arrowvert A \Arrowvert_F = (tr(A^TA))^{1/2} = \lgroup \sum_{i=1}^m \sum_{j=1}^n A_{ij}^2 \rgroup ^{1/2}</script><br>&#x77E9;&#x9635;&#x7684; Frobenius &#x8303;&#x6570;&#x5C31;&#x662F;&#x5C06;&#x77E9;&#x9635;&#x5F20;&#x6210;&#x5411;&#x91CF;&#x540E;&#x7684; L2 &#x8303;&#x6570;&#xFF0C;&#x5176;&#x5B9E;&#x5C31;&#x662F;&#x6240;&#x6709;&#x5143;&#x7D20;&#x7684;&#x5E73;&#x65B9;&#x548C;&#x518D;&#x5F00;&#x65B9;&#x3002;</p>
</li>
<li><p>Page402: &#x4F4E;&#x79E9;&#x77E9;&#x9635;&#x8FD1;&#x4F3C;&#x95EE;&#x9898;</p>
<p>&#x7ED9;&#x5B9A;&#x4E00;&#x4E2A;&#x79E9;&#x4E3A; r &#x7684;&#x77E9;&#x9635; A&#xFF0C;&#x6B32;&#x6C42;&#x5176;&#x6700;&#x4F18; k &#x79E9;&#x8FD1;&#x4F3C;&#x77E9;&#x9635; A&apos;&#xFF08;k &#x2264; r&#xFF09;&#xFF0C;&#x8FD9;&#x6837;&#x7684;&#x95EE;&#x9898;&#x79F0;&#x4E3A;&#x4F4E;&#x79E9;&#x77E9;&#x9635;&#x8FD1;&#x4F3C;&#x95EE;&#x9898;&#x3002;<br>&#x8BE5;&#x95EE;&#x9898;&#x53EF;&#x4EE5;&#x5F62;&#x5F0F;&#x5316;&#x4E3A;&#xFF1A;<br><script type="math/tex; ">min_{A' \in R^{m*n}} \ \ \Arrowvert A - A' \Arrowvert_F, \ \ \ s.t. rank(A') = k</script><br>&#x8BE5;&#x95EE;&#x9898;&#x53EF;&#x4EE5;&#x4F7F;&#x7528;&#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3;&#xFF1A;&#x5BF9;&#x77E9;&#x9635; A &#x8FDB;&#x884C;&#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3;&#x540E;&#xFF0C;&#x5C06; &#x3A3; &#x77E9;&#x9635;&#xFF08;&#x89C1;&#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3;&#xFF09;&#x7684; r-k &#x4E2A;&#x6700;&#x5C0F;&#x7684;&#x5947;&#x5F02;&#x503C;&#x7F6E;&#x96F6;&#x83B7;&#x5F97;&#x77E9;&#x9635; &#x3A3;_k&#xFF0C;A_k = U_k &#x3A3;_k V_k^T &#x5C31;&#x662F;&#x6700;&#x4F18;&#x89E3;&#xFF0C;&#x5176;&#x4E2D; U_k &#x548C; V_k &#x5206;&#x522B;&#x662F; U &#x548C; V &#x524D; k &#x5217;&#x7EC4;&#x6210;&#x7684;&#x77E9;&#x9635;&#x3002;&#x8FD9;&#x4E2A;&#x7ED3;&#x679C;&#x4E5F;&#x79F0;&#x4E3A; Eckart-Young-Mirsky &#x5B9A;&#x7406;&#x3002;</p>
</li>
<li><p>Page402: &#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3;&#xFF08;Singular Value Decomposition&#xFF0C;&#x7B80;&#x79F0; SVD&#xFF09;</p>
<p>&#x5BF9;&#x4EFB;&#x610F;&#x77E9;&#x9635; <script type="math/tex; ">A \in \mathbb{R}^{m\times n}</script> &#x90FD;&#x53EF;&#x5206;&#x89E3;&#x4E3A;&#xFF1A;<script type="math/tex; ">A = U\sum V^T</script>&#xFF0C;&#x5176;&#x4E2D;&#xFF0C;<script type="math/tex; ">U \in \mathbb{R}^{m\times m}</script> &#x662F;&#x6EE1;&#x8DB3; <script type="math/tex; ">U^TU=I</script> &#x7684; m &#x9636;&#x9149;&#x77E9;&#x9635;&#xFF08;unitary matrix&#xFF09;&#xFF1B;<script type="math/tex; ">V \in \mathbb{R}^{n \times n}</script> &#x662F;&#x6EE1;&#x8DB3; <script type="math/tex; ">V^TV=I</script> &#x7684; n &#x9636;&#x9149;&#x77E9;&#x9635;&#xFF1B;<script type="math/tex; ">\sum \in \mathbb{R}^{m \times n}</script> &#x662F; m&#xD7;n &#x7684;&#x77E9;&#x9635;&#xFF0C;&#x5176;&#x4E2D; <script type="math/tex; ">(\sum)_{ii} = \sigma_i</script> &#x4E14;&#x5176;&#x4ED6;&#x4F4D;&#x7F6E;&#x7684;&#x5143;&#x7D20;&#x5747;&#x4E3A; 0&#xFF0C;<script type="math/tex; ">\sigma_i</script> &#x4E3A;&#x975E;&#x8D1F;&#x5B9E;&#x6570;&#x4E14;&#x6EE1;&#x8DB3; <script type="math/tex; ">\sigma_1 \ge \sigma_2 \ge ... \ge 0</script>&#x3002;</p>
</li>
<li><p>Page403: &#x62C9;&#x683C;&#x6717;&#x65E5;&#x4E58;&#x5B50;&#x6CD5;&#xFF08;Lagrange multipliers&#xFF09;</p>
<p>&#x62C9;&#x683C;&#x6717;&#x65E5;&#x4E58;&#x5B50;&#x6CD5;&#x662F;&#x4E00;&#x79CD;&#x5BFB;&#x627E;&#x591A;&#x5143;&#x51FD;&#x6570;&#x5728;&#x4E00;&#x7EC4;&#x7EA6;&#x675F;&#x4E0B;&#x7684;&#x6781;&#x503C;&#x7684;&#x65B9;&#x6CD5;&#x3002;&#x901A;&#x8FC7;&#x5F15;&#x5165;&#x62C9;&#x683C;&#x6717;&#x65E5;&#x4E58;&#x5B50;&#xFF0C;&#x53EF;&#x5C06;&#x6709; d &#x4E2A;&#x53D8;&#x91CF;&#x4E0E; k &#x4E2A;&#x7EA6;&#x675F;&#x6761;&#x4EF6;&#x7684;&#x6700;&#x4F18;&#x5316;&#x95EE;&#x9898;&#x8F6C;&#x5316;&#x4E3A;&#x5177;&#x6709; d+k &#x4E2A;&#x53D8;&#x91CF;&#x7684;&#x65E0;&#x7EA6;&#x675F;&#x4F18;&#x5316;&#x95EE;&#x9898;&#x6C42;&#x89E3;&#x3002;&#x6709;&#x7B49;&#x5F0F;&#x7EA6;&#x675F;&#x548C;&#x4E0D;&#x7B49;&#x5F0F;&#x7EA6;&#x675F;&#x4E24;&#x79CD;&#x3002;<br>&#x4EE5;&#x7B49;&#x5F0F;&#x7EA6;&#x675F;&#x7684;&#x4F18;&#x5316;&#x95EE;&#x9898;&#x4E3A;&#x4F8B;&#x3002;&#x5047;&#x5B9A; x &#x4E3A; d &#x7EF4;&#x5411;&#x91CF;&#xFF0C;&#x8981;&#x6C42; x &#x7684;&#x67D0;&#x4E2A;&#x53D6;&#x503C; x* &#x4F7F;&#x76EE;&#x6807;&#x51FD;&#x6570; f(x) &#x6700;&#x5C0F;&#x4E14;&#x540C;&#x65F6;&#x6EE1;&#x8DB3; g(x)=0 &#x7684;&#x7EA6;&#x675F;&#x3002;&#x4ECE;&#x51E0;&#x4F55;&#x89D2;&#x5EA6;&#x770B;&#x8BE5;&#x95EE;&#x9898;&#x7684;&#x76EE;&#x6807;&#x662F;&#x5728;&#x7531;&#x65B9;&#x7A0B; g(x)=0 &#x786E;&#x5B9A;&#x7684; d-1 &#x7EF4;&#x66F2;&#x9762;&#x4E0A;&#x5BFB;&#x627E;&#x80FD;&#x4F7F;&#x76EE;&#x6807;&#x51FD;&#x6570; f(x) &#x6700;&#x5C0F;&#x5316;&#x7684;&#x70B9;&#x3002;&#x6B64;&#x65F6;&#x5F88;&#x5BB9;&#x6613;&#x5F97;&#x51FA;&#x5728;&#x6700;&#x4F18;&#x70B9;&#x76EE;&#x6807;&#x51FD;&#x6570;&#x4E0E;&#x7EA6;&#x675F;&#x51FD;&#x6570;&#x76F8;&#x5207;&#xFF08;&#x5373;&#x76EE;&#x6807;&#x51FD;&#x6570;&#x5728;&#x8BE5;&#x70B9;&#x7684;&#x68AF;&#x5EA6;&#x6B63;&#x4EA4;&#x4E8E;&#x7EA6;&#x675F;&#x66F2;&#x9762;&#xFF09;&#x3002;&#x7531;&#x6B64;&#x53EF;&#x77E5;&#xFF0C;&#x5728;&#x6700;&#x4F18;&#x70B9;&#xFF0C;&#x68AF;&#x5EA6; <script type="math/tex; ">\nabla g(x), \nabla f(x)</script> &#x65B9;&#x5411;&#x76F8;&#x540C;&#x6216;&#x76F8;&#x53CD;&#xFF1A;&#xFF0C;&#x5373;&#x5B58;&#x5728; &#x3BB; &#x2260; 0 &#x4F7F;&#x5F97; <script type="math/tex; ">\nabla f(x^*) + \lambda \nabla g(x^*) = 0</script>&#xFF0C;&#x3BB; &#x79F0;&#x4E3A;&#x62C9;&#x683C;&#x6717;&#x65E5;&#x4E58;&#x5B50;&#xFF0C;&#x5B9A;&#x4E49;&#x62C9;&#x683C;&#x6717;&#x65E5;&#x51FD;&#x6570;&#x4E3A;&#xFF1A;<script type="math/tex; ">L(x, \lambda) = f(x) + \lambda g(x)</script>&#x3002;</p>
</li>
<li><p>Page405: &#x5BF9;&#x5076;&#x51FD;&#x6570;&#xFF08;dual function&#xFF09;</p>
<p>&#x5C06;&#x4F18;&#x5316;&#x95EE;&#x9898;&#x7684;&#x7EA6;&#x675F;&#x63A8;&#x5E7F;&#x5230;&#x591A;&#x4E2A;&#xFF1A;&#x5177;&#x6709; m &#x4E2A;&#x7B49;&#x5F0F;&#x7EA6;&#x675F;&#x548C; n &#x4E2A;&#x4E0D;&#x7B49;&#x5F0F;&#x7EA6;&#x675F;&#xFF0C;&#x4E14;&#x53EF;&#x884C;&#x57DF; <script type="math/tex; ">\mathbb{D} \subset \mathbb{R}^d </script> &#x975E;&#x7A7A;&#x7684;&#x4F18;&#x5316;&#x95EE;&#x9898;&#xFF1A;<br><script type="math/tex; ">min_x f(x) \ \ s.t.\ \ h_i(x) = 0\ (i=1,...m);\ g_j(x) \le 0\ (j=1,...n)</script><br>&#x8BE5;&#x95EE;&#x9898;&#x4E3A;&#x4F18;&#x5316;&#x95EE;&#x9898;&#x7684;&#x4E3B;&#x95EE;&#x9898;&#xFF08;primal problem&#xFF09;&#xFF0C;&#x76F8;&#x5E94;&#x7684;&#x62C9;&#x683C;&#x6717;&#x65E5;&#x51FD;&#x6570;&#x4E3A;&#xFF1A;<br><script type="math/tex; ">L(x,\lambda,\mu) = f(x) + \sum_{i=1}^m \lambda_i h_i(x) + \sum_{j=1}^n \mu_j g_j(x)</script>&#xFF0C;<br>&#x5176;&#x5BF9;&#x5076;&#x51FD;&#x6570;&#x5B9A;&#x4E49;&#x4E3A;&#xFF1A;<br><script type="math/tex; ">\Gamma(\lambda, \mu) = \inf_{x\in D} L (x, \lambda, \mu) = \inf_{x\in D} \lgroup f(x) + \sum_{i=1}^m \lambda_i h_i(x) + \sum_{j=1}^n \mu_j g_j(x)\rgroup</script>&#x3002;<br>&#x5BF9;&#x5076;&#x51FD;&#x6570;&#x7ED9;&#x51FA;&#x4E86;&#x4E3B;&#x95EE;&#x9898;&#x7684;&#x6700;&#x4F18;&#x503C;&#x4E0B;&#x754C;&#xFF0C;&#x56E0;&#x4E3A;&#x82E5; x* &#x4E3A;&#x4E3B;&#x95EE;&#x9898;&#x53EF;&#x884C;&#x57DF;&#x7684;&#x70B9;&#xFF0C;&#x5BF9;&#x4EFB;&#x610F; <script type="math/tex; ">\mu \succeq 0, \lambda</script>&#xFF0C;&#x90FD;&#x6709; <script type="math/tex; ">\sum_{i=1}^m \lambda_i h_i(x) + \sum_{j=1}^n \mu_j g_j(x) \le 0</script>&#xFF0C;&#x8FDB;&#x800C;&#x6709; <script type="math/tex; ">\Gamma(\lambda,\mu) \le L(x^*, \lambda, \mu) \le f(x^*)</script>&#x3002;</p>
</li>
<li><p>Page406: &#x4E8C;&#x6B21;&#x89C4;&#x5212;&#xFF08;Quadratic Programming&#xFF0C;&#x7B80;&#x79F0; QP&#xFF09;</p>
<p>&#x4E00;&#x7C7B;&#x5178;&#x578B;&#x7684;&#x4F18;&#x5316;&#x95EE;&#x9898;&#xFF0C;&#x5305;&#x62EC;&#x51F8;&#x4E8C;&#x6B21;&#x4F18;&#x5316;&#x548C;&#x975E;&#x51F8;&#x4E8C;&#x6B21;&#x4F18;&#x5316;&#x3002;&#x76EE;&#x6807;&#x51FD;&#x6570;&#x662F;&#x53D8;&#x91CF;&#x7684;&#x4E8C;&#x6B21;&#x51FD;&#x6570;&#xFF0C;&#x7EA6;&#x675F;&#x6761;&#x4EF6;&#x662F;&#x53D8;&#x91CF;&#x7684;&#x7EBF;&#x6027;&#x4E0D;&#x7B49;&#x5F0F;&#x3002;&#x5047;&#x5B9A;&#x53D8;&#x91CF;&#x4E2A;&#x6570;&#x4E3A; d&#xFF0C;&#x7EA6;&#x675F;&#x6761;&#x4EF6;&#x4E2A;&#x6570;&#x4E3A; m&#xFF0C;&#x6807;&#x51C6;&#x7684;&#x4E8C;&#x6B21;&#x89C4;&#x5212;&#x95EE;&#x9898;&#x5F62;&#x5982;&#xFF1A;<br><script type="math/tex; ">\min_x \ \  \frac{1}{2} x^TQx + c^Tx, \ \ s.t. Ax \le b</script><br>&#x5176;&#x4E2D;&#xFF0C;x &#x4E3A; d &#x7EF4;&#x5411;&#x91CF;&#xFF0C; Q &#x2208; R &#x4E3A;&#x5B9E;&#x5BF9;&#x79F0;&#x77E9;&#x9635;&#xFF0C;A &#x2208; R &#x4E3A;&#x5B9E;&#x77E9;&#x9635;&#xFF0C;b &#x2208; R &#x548C; c &#x2208; R &#x4E3A;&#x5B9E;&#x5411;&#x91CF;&#xFF0C;Ax &#x2264; b &#x7684;&#x6BCF;&#x4E00;&#x884C;&#x5BF9;&#x5E94;&#x4E00;&#x4E2A;&#x7EA6;&#x675F;&#x3002;</p>
</li>
<li><p>Page407: &#x534A;&#x6B63;&#x5B9A;&#x89C4;&#x5212;&#xFF08;Seme-Definite Programming&#xFF0C;&#x7B80;&#x79F0; SDP&#xFF09;</p>
<p>&#x662F;&#x4E00;&#x7C7B;&#x51F8;&#x4F18;&#x5316;&#x95EE;&#x9898;&#xFF0C;&#x5176;&#x4E2D;&#x7684;&#x53D8;&#x91CF;&#x53EF;&#x7EC4;&#x7EC7;&#x6210;&#x534A;&#x6B63;&#x5B9A;&#x5BF9;&#x79F0;&#x77E9;&#x9635;&#x5F62;&#x5F0F;&#xFF0C;&#x4E14;&#x4F18;&#x5316;&#x95EE;&#x9898;&#x7684;&#x76EE;&#x6807;&#x51FD;&#x6570;&#x548C;&#x7EA6;&#x675F;&#x90FD;&#x662F;&#x8FD9;&#x4E9B;&#x53D8;&#x91CF;&#x7684;&#x7EBF;&#x6027;&#x51FD;&#x6570;&#x3002;<br>&#x7ED9;&#x5B9A; d&#xD7;d &#x7684;&#x5BF9;&#x79F0;&#x77E9;&#x9635; <strong>X, C</strong>&#xFF0C;<script type="math/tex; ">C·X = \sum_{i=1}^d\sum_{j=1}^dC_{ij}X_{ij}</script>&#xFF0C;<br>&#x82E5; Ai(i=1,...,m) &#x4E5F;&#x662F; d&#xD7;d &#x7684;&#x5BF9;&#x79F0;&#x77E9;&#x9635;&#xFF0C;bi(i=1,2,...,m) &#x4E3A; m &#x4E2A;&#x5B9E;&#x6570;&#xFF0C;&#x5219;&#x534A;&#x6B63;&#x5B9A;&#x89C4;&#x5212;&#x95EE;&#x9898;&#x5F62;&#x5982;&#xFF1A;<br><script type="math/tex; ">min_X C · X; \ \ s.t. \ A_i \cdot X = b_i; \ \ i = 1,2,...,m, X \succeq 0</script></p>
</li>
</ul>
<ul>
<li><p>Page409: &#x4F2F;&#x52AA;&#x5229;&#x5206;&#x5E03;&#xFF08;Bernoulli distribution&#xFF09;</p>
<p>&#x5173;&#x4E8E;&#x5E03;&#x5C14;&#x53D8;&#x91CF; x &#x2208; {0,1} &#x7684;&#x6982;&#x7387;&#x5206;&#x5E03;&#xFF0C;&#x5176;&#x8FDE;&#x7EED;&#x53C2;&#x6570; &#x3BC; &#x2208; [0,1] &#x8868;&#x793A;&#x53D8;&#x91CF; x=1 &#x7684;&#x6982;&#x7387;&#x3002;<br><script type="math/tex; ">P(x|\mu) = Bern(x|\mu) = \mu^x(1-\mu)^{(1-x)}</script><br><script type="math/tex; ">\mathbb{E}[x] = \mu; var[x] = \mu(1-\mu)</script></p>
</li>
<li><p>Page409: &#x5747;&#x5300;&#x5206;&#x5E03;&#xFF08;uniform distribution&#xFF09;</p>
<p>&#x5173;&#x4E8E;&#x5B9A;&#x4E49;&#x5728;&#x533A;&#x95F4; <code>[a,b](a&lt;b)</code> &#x4E0A;&#x8FDE;&#x7EED;&#x53D8;&#x91CF;&#x7684;&#x7B80;&#x5355;&#x6982;&#x7387;&#x5206;&#x5E03;&#x3002;<br><script type="math/tex; ">p(x|a,b) = U(x|a,b) = \frac{1}{b-a}</script><br><script type="math/tex; ">\mathbb{E}[x] = \frac{a+b}{2}; var[x] = \frac{(b-a)^2}{12}</script></p>
</li>
<li><p>Page410: &#x591A;&#x9879;&#x5206;&#x5E03;&#xFF08;multinominal distribution&#xFF09;</p>
<p>&#x5C06;&#x4F2F;&#x52AA;&#x5229;&#x5206;&#x5E03;&#x7531;&#x5355;&#x53D8;&#x91CF;&#x6269;&#x5C55;&#x4E3A; d &#x7EF4;&#xFF0C;&#x5E76;&#x5728;&#x6B64;&#x57FA;&#x7840;&#x4E0A;&#x6269;&#x5C55;&#x4E8C;&#x9879;&#x5206;&#x5E03;&#x5C31;&#x5F97;&#x5230;&#x591A;&#x9879;&#x5206;&#x5E03;&#xFF0C;&#x5B83;&#x63CF;&#x8FF0;&#x4E86;&#x5728; N &#x6B21;&#x72EC;&#x7ACB;&#x5B9E;&#x9A8C;&#x4E2D;&#x6709; mi &#x6B21; xi=1 &#x7684;&#x6982;&#x7387;&#x3002;<br><script type="math/tex; ">P(m_1,m_2,...,m_d|N,\mu) = Mult(m_1,m_2,...,m_d|N,\mu) = \frac{N!}{m_1!m_2!...m_d!} \prod_{i=1}^d \mu_i^{m_i}</script><br><script type="math/tex; ">\mathbb{E}[m_i] = N\mu_i; \ var[m_i] = N\mu_i(1-\mu_i); \ cov[m_j,m_i] = -N\mu_j\mu_i</script></p>
</li>
<li><p>Page410: &#x4E8C;&#x9879;&#x5206;&#x5E03;&#xFF08;binomial distribution&#xFF09;</p>
<p>&#x63CF;&#x8FF0; N &#x6B21;&#x662F;&#x72EC;&#x7ACB;&#x7684;&#x4F2F;&#x52AA;&#x5229;&#x5B9E;&#x9A8C;&#x4E2D;&#x6709; m &#x6B21;&#x6210;&#x529F;&#xFF08;x=1&#xFF09;&#x7684;&#x6982;&#x7387;&#x3002;<br><script type="math/tex; ">P(m|N,\mu) = Bin(m|N,\mu) = {N \choose m} \mu^m (1-\mu)^{N-m}</script></p>
</li>
<li><p>Page411: &#x8D1D;&#x5854;&#x5206;&#x5E03;&#xFF08;Beta distribution&#xFF09;</p>
<p>&#x5173;&#x4E8E;&#x8FDE;&#x7EED;&#x53D8;&#x91CF; &#x3BC; &#x2208; [0,1] &#x7684;&#x6982;&#x7387;&#x5206;&#x5E03;&#xFF0C;&#x7531;&#x4E24;&#x4E2A;&#x53C2;&#x6570; a&gt;0, b&gt;0 &#x786E;&#x5B9A;&#xFF1A;<br><script type="math/tex; ">p(\mu|a,b) = Beta(\mu|a,b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \mu^{a-1} (1-\mu)^{b-1} = \frac{1}{B(a,b)} \mu^{a-1}(1-\mu)^{b-1}</script><br><script type="math/tex; ">\mathbb{E}[\mu] = \frac{a}{a+b}; \ var[\mu] = \frac{ab}{(a+b)^2(a+b+a)}; \ \Gamma(a) = \int_{0}^{+\infty}t^{a-1}e^{-t}dt</script><br>&#x5F53; a=b=1 &#x65F6;&#xFF0C;&#x8D1D;&#x5854;&#x5206;&#x5E03;&#x9000;&#x5316;&#x4E3A;&#x5747;&#x5300;&#x5206;&#x5E03;&#x3002;</p>
</li>
<li><p>Page412: &#x72C4;&#x5229;&#x514B;&#x96F7;&#x5206;&#x5E03;&#xFF08;Dirichlet distribution&#xFF09;</p>
<p>&#x5173;&#x4E8E;&#x4E00;&#x7EC4; d &#x4E2A;&#x8FDE;&#x7EED;&#x53D8;&#x91CF; &#x3BC;i &#x2208; [0,1] &#x7684;&#x6982;&#x7387;&#x5206;&#x5E03;&#xFF0C;<script type="math/tex; ">\sum_{i=1}^d \mu_i = 1</script>&#x3002;&#x4EE4; <script type="math/tex; ">\mu = (\mu_1,...,\mu_d)</script>&#xFF0C;&#x53C2;&#x6570; <script type="math/tex; ">\alpha = (\alpha_1,...,\alpha_d), \ \alpha_i>0, \hat{\alpha} = \sum_{i=1}^d \alpha_i</script><br><script type="math/tex; ">p(\mu|\alpha) = Dir(\mu|\alpha) = \frac{\Gamma(\hat{\alpha})}{\Gamma(\alpha_1)...\Gamma(\alpha_i）} \prod_{i=1}^d \mu_i^{(\alpha_i-1)}</script><br><script type="math/tex; ">\mathbb{E}[\mu_i] = \frac{\alpha_i}{\hat{\alpha}}, \ var[\mu_i] = \frac{\alpha_i(\hat{\alpha}-\alpha_i)}{\hat{\alpha}^2(\hat{\alpha}+1)}, \ cov[\mu_j,\mu_i] = \frac{\alpha_j\alpha_i}{\hat{\alpha}^2(\hat{\alpha}+1)}</script><br>&#x5F53; d=2 &#x65F6;&#xFF0C;&#x72C4;&#x5229;&#x514B;&#x96F7;&#x5206;&#x5E03;&#x9000;&#x5316;&#x4E3A;&#x8D1D;&#x5854;&#x5206;&#x5E03;&#x3002;</p>
</li>
<li><p>Page412: &#x9AD8;&#x65AF;&#x5206;&#x5E03;&#xFF08;Gaussian distribution&#xFF09;</p>
<p>&#x4EA6;&#x79F0;&#x6B63;&#x6001;&#x5206;&#x5E03;&#xFF08;normal distribution&#xFF09;&#xFF0C;&#x662F;&#x5E94;&#x7528;&#x6700;&#x5E7F;&#x6CDB;&#x7684;&#x8FDE;&#x7EED;&#x6982;&#x7387;&#x5206;&#x5E03;&#x3002;<br>&#x5BF9;&#x4E8E;&#x5355;&#x53D8;&#x91CF; x &#x2208; (-&#x221E;, +&#x221E;)&#xFF0C;&#x9AD8;&#x65AF;&#x5206;&#x5E03;&#x7684;&#x53C2;&#x6570;&#x4E3A;&#x5747;&#x503C; &#x3BC; &#x2208; (-&#x221E;, +&#x221E;) &#x548C; &#x65B9;&#x5DEE; &#x3C3;^2 &gt; 0&#x3002;<br><script type="math/tex; ">p(x|\mu,\sigma^2) = \mathcal{N}(x|\mu,\sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp \{ -\frac{(x-\mu)^2}{2\sigma^2} \}</script><br><script type="math/tex; ">\mathbb{E}=\mu, \ var[x]=\sigma^2</script><br>&#x5BF9;&#x4E8E; d &#x7EF4;&#x5411;&#x91CF; <strong>x</strong>&#xFF0C;&#x591A;&#x5143;&#x9AD8;&#x65AF;&#x5206;&#x5E03;&#x7684;&#x53C2;&#x6570;&#x4E3A; d &#x7EF4;&#x5747;&#x503C;&#x5411;&#x91CF; <strong>&#x3BC;</strong> &#x548C; d&#xD7;d &#x7684;&#x5BF9;&#x79F0;&#x6B63;&#x5B9A;&#x534F;&#x65B9;&#x5DEE;&#x77E9;&#x9635; <strong>&#x3A3;</strong>&#x3002;<br><script type="math/tex; ">p(x|\mu,\sum) = \mathcal{N}(x|\mu,\sum) = \frac{1}{\sqrt{2\pi^d \det(\sum)}} \exp \{ -\frac{1}{2}(x-\mu)^T {\sum}^{-1}(x-\mu) \}</script><br><script type="math/tex; ">\mathbb{E}=\mu, \ var[x]=\sum</script></p>
</li>
<li><p>Page412: &#x6B63;&#x6001;&#x5206;&#x5E03;&#xFF08;normal distribution&#xFF09;</p>
<p>&#x540C;&#x9AD8;&#x65AF;&#x5206;&#x5E03;&#x3002;</p>
</li>
<li><p>Page413: &#x5171;&#x8F6D;&#x5206;&#x5E03;&#xFF08;conjugate distribution&#xFF09;</p>
<p>&#x5047;&#x8BBE;&#x53D8;&#x91CF; x &#x670D;&#x4ECE;&#x5206;&#x5E03; P(x|&#x398;)&#xFF0C;&#x5176;&#x4E2D; &#x398; &#x4E3A;&#x53C2;&#x6570;&#xFF0C;X={x1,x2,...,xm} &#x4E3A;&#x53D8;&#x91CF; x &#x7684;&#x89C2;&#x6D4B;&#x6837;&#x672C;&#xFF0C;&#x5047;&#x8BBE;&#x53C2;&#x6570; &#x398; &#x670D;&#x4ECE;&#x5148;&#x9A8C;&#x5206;&#x5E03; &#x220F;(&#x398;)&#x3002;<br>&#x82E5;&#x7531;&#x5148;&#x9A8C;&#x5206;&#x5E03; &#x220F;(&#x398;) &#x548C;&#x62BD;&#x6837;&#x5206;&#x5E03; P(X|&#x398;) &#x51B3;&#x5B9A;&#x7684;&#x540E;&#x9A8C;&#x5206;&#x5E03; F(&#x398;|X) &#x4E0E; &#x220F;(&#x398;) &#x662F;&#x540C;&#x79CD;&#x7C7B;&#x578B;&#x7684;&#x5206;&#x5E03;&#xFF0C;&#x5219;&#x79F0;&#x5148;&#x9A8C;&#x5206;&#x5E03; &#x220F;(&#x398;) &#x4E3A;&#x5206;&#x5E03; P(X|&#x398;) &#x6216; P(x|&#x398;) &#x7684;&#x5171;&#x8F6D;&#x5206;&#x5E03;&#x3002;</p>
</li>
<li><p>Page414: &#x76F8;&#x5BF9;&#x71B5;&#xFF08;relative entropy&#xFF09;</p>
<p>&#x4EA6;&#x79F0; KL &#x6563;&#x5EA6;&#x6216;&#x4FE1;&#x606F;&#x6563;&#x5EA6;&#xFF0C;&#x53EF;&#x7528;&#x4E8E;&#x5EA6;&#x91CF;&#x4E24;&#x4E2A;&#x6982;&#x7387;&#x5206;&#x5E03;&#x4E4B;&#x95F4;&#x7684;&#x5DEE;&#x5F02;&#x3002;&#x7ED9;&#x5B9A;&#x4E24;&#x4E2A;&#x6982;&#x7387;&#x5206;&#x5E03; P &#x548C; Q&#xFF0C;&#x4E8C;&#x8005;&#x4E4B;&#x95F4;&#x7684;&#x76F8;&#x5BF9;&#x71B5;&#x5B9A;&#x4E49;&#x4E3A;&#xFF1A;<br><script type="math/tex; ">KL(P||Q) = \int_{-\infty}^{+\infty} p(x)\log\frac{p(x)}{q(x)}dx</script><br>&#x5176;&#x4E2D; p(x) &#x548C; q(x) &#x5206;&#x522B;&#x4E3A; P &#x548C; Q &#x7684;&#x6982;&#x7387;&#x5BC6;&#x5EA6;&#x51FD;&#x6570;&#x3002;<br>&#x901A;&#x4FD7;&#x5730;&#x8BF4;&#xFF0C;&#x7528;&#x5206;&#x5E03; Q &#x7684;&#x6700;&#x4F73;&#x4FE1;&#x606F;&#x4F20;&#x9012;&#x65B9;&#x5F0F;&#x6765;&#x4F20;&#x8FBE;&#x5206;&#x5E03; P&#xFF0C;&#x6BD4;&#x7528;&#x5206;&#x5E03; P &#x81EA;&#x5DF1;&#x7684;&#x6700;&#x4F73;&#x4FE1;&#x606F;&#x65B9;&#x5F0F;&#x4F20;&#x8FBE;&#x5E73;&#x5747;&#x591A;&#x8017;&#x8D39;&#x7684;&#x4FE1;&#x606F;&#x957F;&#x5EA6;&#x4E3A; KL &#x6563;&#x5EA6;&#x3002;</p>
</li>
<li><p>Page414: &#x4FE1;&#x606F;&#x6563;&#x5EA6;&#xFF08;information divergence&#xFF09;</p>
<p>&#x540C;&#x76F8;&#x5BF9;&#x71B5;&#x3002;</p>
</li>
<li><p>Page415: &#x4EA4;&#x53C9;&#x71B5;&#xFF08;cross entropy&#xFF09;</p>
<p>KL &#x6563;&#x5EA6;&#x5C55;&#x5F00;&#x53EF;&#x5F97;&#xFF1A;<br><script type="math/tex; ">KL(P||Q) = \int_{-\infty}^{+\infty} p(x)\log p(x)dx - \int_{-\infty}^{+\infty} p(x)\log q(x)dx = -H(P) + H(P,Q)</script><br>&#x5176;&#x4E2D; H(P) &#x4E3A;&#x71B5;&#xFF0C;H(P,Q) &#x4E3A; P &#x548C; Q &#x7684;&#x4EA4;&#x53C9;&#x71B5;&#x3002;
&#x901A;&#x4FD7;&#x5730;&#x8BF4;&#xFF0C;&#x7528;&#x5206;&#x5E03; Q &#x7684;&#x6700;&#x4F73;&#x4FE1;&#x606F;&#x4F20;&#x9012;&#x65B9;&#x5F0F;&#x4F20;&#x8FBE;&#x5206;&#x5E03; P &#x4E2D;&#x968F;&#x673A;&#x62BD;&#x9009;&#x7684;&#x4E00;&#x4E2A;&#x4E8B;&#x4EF6;&#xFF0C;&#x6240;&#x9700;&#x7684;&#x5E73;&#x5747;&#x4FE1;&#x606F;&#x957F;&#x5EA6;&#x4E3A;&#x4EA4;&#x53C9;&#x71B5;&#x3002;</p>
</li>
<li><p>Page415: &#x71B5;&#xFF08;entropy&#xFF09;</p>
<p>&#x71B5;&#x662F;&#x5BF9;&#x6574;&#x4E2A;&#x4E8B;&#x4EF6;&#x4FE1;&#x606F;&#x91CF;&#x7684;&#x91CF;&#x5316;&#xFF0C;&#x4F20;&#x8FBE;&#x4FE1;&#x606F;&#x6240;&#x9700;&#x7684;&#x6700;&#x4F18;&#x5E73;&#x5747;&#x4FE1;&#x606F;&#x957F;&#x5EA6;&#x4E3A;&#x9999;&#x519C;&#x71B5;&#x3002;<br><script type="math/tex; ">H(P) = \sum_xP(x)\log\frac{1}{P(x)}</script></p>
</li>
</ul>
<hr>
<p>&#x9644;&#xFF1A;&#x4E00;&#x4E9B;&#x4E0D;&#x9519;&#x7684;&#x5B66;&#x4E60;&#x8D44;&#x6599;</p>
<ul>
<li><p>&#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3;</p>
<ul>
<li><a href="https://blog.csdn.net/u010099080/article/details/68060274" target="_blank">&#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3; SVD &#x7684;&#x6570;&#x5B66;&#x89E3;&#x91CA; - CSDN &#x535A;&#x5BA2;</a></li>
<li><a href="https://www.zhihu.com/question/22237507" target="_blank">(3 &#x6761;&#x6D88;&#x606F;) &#x5947;&#x5F02;&#x503C;&#x7684;&#x7269;&#x7406;&#x610F;&#x4E49;&#x662F;&#x4EC0;&#x4E48;&#xFF1F; - &#x77E5;&#x4E4E;</a></li>
<li><a href="http://www.cnblogs.com/LeftNotEasy/archive/2011/01/19/1939687.html" target="_blank">&#x673A;&#x5668;&#x5B66;&#x4E60;&#x4E2D;&#x7684;&#x6570;&#x5B66; (5)- &#x5F3A;&#x5927;&#x7684;&#x77E9;&#x9635;&#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3; (SVD) &#x53CA;&#x5176;&#x5E94;&#x7528; - LeftNotEasy - &#x535A;&#x5BA2;&#x56ED;</a></li>
<li><a href="https://blog.csdn.net/zhongkejingwang/article/details/43053513" target="_blank">&#x5947;&#x5F02;&#x503C;&#x5206;&#x89E3; (SVD) &#x539F;&#x7406;&#x8BE6;&#x89E3;&#x53CA;&#x63A8;&#x5BFC; - CSDN &#x535A;&#x5BA2;</a></li>
</ul>
</li>
<li><p>&#x62C9;&#x683C;&#x6717;&#x65E5;&#x4E58;&#x5B50;&#x6CD5;</p>
<ul>
<li><a href="https://www.zhihu.com/question/38586401" target="_blank">(3 &#x6761;&#x6D88;&#x606F;) &#x62C9;&#x683C;&#x6717;&#x65E5;&#x4E58;&#x5B50;&#x6CD5;&#x5982;&#x4F55;&#x7406;&#x89E3;&#xFF1F; - &#x77E5;&#x4E4E;</a></li>
<li><a href="http://www.cnblogs.com/mo-wang/p/4775548.html" target="_blank">&#x3010;&#x6574;&#x7406;&#x3011;&#x6DF1;&#x5165;&#x7406;&#x89E3;&#x62C9;&#x683C;&#x6717;&#x65E5;&#x4E58;&#x5B50;&#x6CD5;&#xFF08;Lagrange Multiplier) &#x548C; KKT &#x6761;&#x4EF6; - mo_wang - &#x535A;&#x5BA2;&#x56ED;</a></li>
<li><a href="http://www.slimy.com/~steuard/teaching/tutorials/Lagrange.html" target="_blank">An Introduction to Lagrange Multipliers</a></li>
</ul>
</li>
<li><p>&#x68AF;&#x5EA6;</p>
<ul>
<li><a href="https://www.matongxue.com/madocs/222.html#/madoc" target="_blank">&#x6587;&#x7AE0;</a></li>
<li><a href="https://zhuanlan.zhihu.com/p/24913912" target="_blank">&#x4E3A;&#x4EC0;&#x4E48;&#x68AF;&#x5EA6;&#x53CD;&#x65B9;&#x5411;&#x662F;&#x51FD;&#x6570;&#x503C;&#x5C40;&#x90E8;&#x4E0B;&#x964D;&#x6700;&#x5FEB;&#x7684;&#x65B9;&#x5411;&#xFF1F;</a></li>
<li><a href="https://www.youtube.com/watch?v=npkl19rcpdY" target="_blank">&#x68AF;&#x5EA6; - YouTube</a></li>
</ul>
</li>
<li><p>&#x6B63;&#x5B9A;&#x77E9;&#x9635;&#x548C;&#x534A;&#x6B63;&#x5B9A;&#x77E9;&#x9635;</p>
<ul>
<li><a href="https://blog.csdn.net/asd136912/article/details/79146151" target="_blank">&#x6B63;&#x5B9A;&#x77E9;&#x9635;&#x4E0E;&#x534A;&#x6B63;&#x5B9A;&#x77E9;&#x9635;&#x5B9A;&#x4E49;&#x6027;&#x8D28;&#x4E0E;&#x7406;&#x89E3; - CSDN &#x535A;&#x5BA2;</a></li>
</ul>
</li>
<li><p>&#x8D1D;&#x5854;&#x5206;&#x5E03;</p>
<ul>
<li><a href="https://blog.csdn.net/a358463121/article/details/52562940" target="_blank">&#x5E26;&#x4F60;&#x7406;&#x89E3; beta &#x5206;&#x5E03; - CSDN &#x535A;&#x5BA2;</a></li>
</ul>
</li>
<li><p>&#x72C4;&#x5229;&#x514B;&#x96F7;&#x5206;&#x5E03;</p>
<ul>
<li><a href="https://www.zhihu.com/question/26751755" target="_blank">(2 &#x6761;&#x6D88;&#x606F;) &#x4EC0;&#x4E48;&#x662F;&#x72C4;&#x5229;&#x514B;&#x96F7;&#x5206;&#x5E03;&#xFF1F;&#x72C4;&#x5229;&#x514B;&#x96F7;&#x8FC7;&#x7A0B;&#x53C8;&#x662F;&#x4EC0;&#x4E48;&#xFF1F; - &#x77E5;&#x4E4E;</a></li>
<li><a href="https://blog.csdn.net/jwh_bupt/article/details/8841644" target="_blank">&#x673A;&#x5668;&#x5B66;&#x4E60;&#x7684;&#x6570;&#x5B66;&#x57FA;&#x7840;&#xFF08;1&#xFF09;--Dirichlet &#x5206;&#x5E03; - CSDN &#x535A;&#x5BA2;</a></li>
<li><a href="http://blog.sciencenet.cn/blog-677221-1051014.html" target="_blank">&#x79D1;&#x5B66;&#x7F51;&#x2014;&#x518D;&#x8C08;&#x5206;&#x5E03;&#x4E4B;&#x5206;&#x5E03;&#xFF08;dirichlet &#x5206;&#x5E03;&#xFF09;- &#x8D1D;&#x53F6;&#x65AF;&#x5206;&#x6790;&#x4E4B; 2 - &#x5F20;&#x5929;&#x84C9;&#x7684;&#x535A;&#x6587;</a></li>
<li><a href="https://xijunlee.github.io/2017/09/09/Dirichlet%E5%88%86%E5%B8%83%E4%B8%8EBeta%E5%88%86%E5%B8%83/" target="_blank">&#x901A;&#x4FD7;&#x7406;&#x89E3; Dirichlet &#x5206;&#x5E03;&#x53CA;&#x5176;&#x5B9E;&#x8DF5; | A Notebook</a></li>
<li><a href="https://www.datalearner.com/blog/1051459673766843" target="_blank">Dirichlet Distribution&#xFF08;&#x72C4;&#x5229;&#x514B;&#x96F7;&#x5206;&#x5E03;&#xFF09;&#x4E0E; Dirichlet Process&#xFF08;&#x72C4;&#x5229;&#x514B;&#x96F7;&#x8FC7;&#x7A0B;&#xFF09; | &#x6570;&#x636E;&#x5B66;&#x4E60;&#x8005;&#x5B98;&#x65B9;&#x7F51;&#x7AD9; (Datalearner)</a></li>
<li><a href="http://emma.memect.com/t/9756da9a47744de993d8df13a26e04e38286c9bc1c5a0d2b259c4564c6613298/LDA" target="_blank">LDA&#x6570;&#x5B66;&#x516B;&#x5366;</a></li>
</ul>
</li>
<li><p>&#x71B5;&#x3001;&#x76F8;&#x5BF9;&#x71B5;&#x3001;&#x4EA4;&#x53C9;&#x71B5;</p>
<ul>
<li><a href="https://medium.com/swlh/shannon-entropy-in-the-context-of-machine-learning-and-ai-24aee2709e32" target="_blank">Shannon entropy in the context of machine learning and AI</a></li>
<li><a href="https://www.jiqizhixin.com/articles/0224" target="_blank">&#x5982;&#x4F55;&#x7406;&#x89E3;KL&#x6563;&#x5EA6;&#x7684;&#x4E0D;&#x5BF9;&#x79F0;&#x6027; | &#x673A;&#x5668;&#x4E4B;&#x5FC3;</a></li>
<li><a href="https://www.bilibili.com/video/av19193502?from=search&amp;seid=9145887951572377038" target="_blank">&#x3010; &#x6DF1;&#x5EA6;&#x5B66;&#x4E60; &#x3011;&#x71B5;&#xFF0C;&#x4EA4;&#x53C9;&#x71B5;&#xFF0C;KL &#x6563;&#x5EA6; Entropy, Cross-Entropy and KL-Divergence</a></li>
</ul>
</li>
</ul>

                                
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